Journal of the
Korean Mathematical Society JKMS

In this paper, we introduce the notion of Gorenstein quasi-resolving subcategories (denoted by $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$) in term of quasi-resolving subcategory $\mathcal{X}$. We define a resolution dimension relative to the Gorenstein quasi-resolving categories $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$. In addition, we study the stability of $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$ and apply the obtained properties to special subcategories and in particular to modules categories. Finally, we use the restricted flat dimension of right $B$-module $M$ to characterize the finitistic dimension of the endomorphism algebra $B$ of a $\mathcal{GQ}_{\mathcal{X}}$-projective $A$-module $M$.

Keywords: $\mathcal{GQ}_{\mathcal{X}}$-projective objects, $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$-resolution, stability, finitistic dimension, endomorphism algebras

MSC numbers: Primary 16D10, 16E05, 16E10, 18G10

Supported by: Weiqing Cao was supported by the Science Foundation of Jiangsu Normal University (No. 21XFRS024). Jiaqun Wei was supported by the National Natural Science Foundation of China (Grant No. 11771212) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.